Suppose there was no gravity and space-time was completely flat. This would be like a completely featureless desert. Such a place has two types of symmetry. The first is called translation symmetry. If you moved from one point in the desert to another, you would not notice any change. The second symmetry is rotation symmetry. If you stood somewhere in the desert and started to turn around, you would again not notice any difference in what you saw. These symmetries are also found in “flat” space-time, the space-time one finds in the absence of any matter.

If one put something into this desert, these symmetries would be broken. Suppose there was a mountain, an oasis and some cacti in the desert, it would look different in different places and in different directions. The same is true of space-time. If one puts objects into a space-time, the translational and rotational symmetries get broken. And introducing objects into a space-time is what produces gravity.

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A black hole is a region of space-time where gravity is strong, space-time is violently distorted and so one expects its symmetries to be broken. However, as one moves away from the black hole, the curvature of space-time gets less and less. Very far away from the black hole, space-time looks very much like flat space-time.

Back in the 1960s, Hermann Bondi, A. W. Kenneth Metzner, M. G. J. van der Burg and Rainer Sachs made the truly remarkable discovery that space-time far away from any matter has an infinite collection of symmetries known as supertranslations. Each of these symmetries is associated with a conserved quantity, known as the supertranslation charges. A conserved quantity is a quantity that does not change as a system evolves. These are generalisations of more familiar conserved quantities. For example, if space-time does not change in time, then energy is conserved. If space-time looks the same at different points in space, then momentum is conserved.

What was remarkable about the discovery of supertranslations is that there are an infinite number of conserved quantities far from a black hole. It is these conservation laws that have given an extraordinary and unexpected insight into process in gravitational physics.

In 2016, together with my collaborators Malcolm Perry and Andy Strominger, I was working on using these new results with their associated conserved quantities to find a possible resolution to the information paradox. We know that the three discernible properties of black holes are their mass, their charge and their angular momentum. These are the classical charges that have been understood for a long time. However, black holes also carry a supertranslation charge. So perhaps black holes have a lot more to them than we first thought. They are not bald or with only three hairs, but actually have a very large amount of supertranslation hair.

This supertranslation hair might encode some of the information about what is inside the black hole. It is likely that these supertranslation charges do not contain all of the information, but the rest might be accounted for by some additional conserved quantities, superrotation charges, associated with some additional related symmetries called superrotations, which are as yet, not well understood. If this is right, and all the information about a black hole can be understood in terms of its “hairs”, then perhaps there is no loss of information. These ideas have just received confirmation with our most recent calculations. Strominger, Perry and myself, together with a graduate student, Sasha Haco, have discovered that these superrotation charges can account for the entire entropy of any black hole. Quantum mechanics continues to hold, and information is stored on the horizon, the surface of the black hole.

The black holes are still characterised only by their overall mass, electric charge and spin outside the event horizon but the event horizon itself contains the information needed to tell us about what has fallen into the black hole in a way that goes beyond these three characteristics the black hole has. People are still working on these issues and therefore the information paradox remains unresolved. But I am optimistic that we are moving towards a solution. Watch this space.